U.S. patent number 5,384,811 [Application Number 07/853,751] was granted by the patent office on 1995-01-24 for method for the transmission of a signal.
This patent grant is currently assigned to Telefunken. Invention is credited to Gerhard Dickopp, Detlef Krahe, Thomas Vaupel.
United States Patent |
5,384,811 |
Dickopp , et al. |
January 24, 1995 |
**Please see images for:
( Certificate of Correction ) ** |
Method for the transmission of a signal
Abstract
The process disclosed enables the "time domain aliasing
cancellation" method to be extended systematically to larger block
overlapping. The boundary conditions which, when using various
modified transforms, the analysis and synthesis windows must comply
with, can thus be given. The transform series must also be included
in the design of each analysis and synthesis window in order to
optimize for a given application, because this changes the boundry
conditions with which an analysis window function can be
determined. Design for analysis and synthesis windows have shown
that analysis and synthesis properties obtained by multiple block
overlapping are significantly better than those obtained by
convential double block overlapping. The systematic method of the
invention offers numerous possibilites for optimizing windows in
special applications.
Inventors: |
Dickopp; Gerhard
(Krefeld-Bockum, DE), Vaupel; Thomas (Essen,
DE), Krahe; Detlef (Kempen, DE) |
Assignee: |
Telefunken (Hanover,
DE)
|
Family
ID: |
25885859 |
Appl.
No.: |
07/853,751 |
Filed: |
August 24, 1992 |
PCT
Filed: |
October 08, 1990 |
PCT No.: |
PCT/EP90/01683 |
371
Date: |
August 24, 1992 |
102(e)
Date: |
August 24, 1992 |
PCT
Pub. No.: |
WO91/05412 |
PCT
Pub. Date: |
April 18, 1991 |
Foreign Application Priority Data
Current U.S.
Class: |
704/203; 375/242;
704/211 |
Current CPC
Class: |
H04B
1/66 (20130101) |
Current International
Class: |
H04B
1/66 (20060101); H04B 001/66 (); H04B 014/04 () |
Field of
Search: |
;375/122,27,25
;381/29,36,37,40,31 |
Other References
"Digital Communications Fundamental and Applications" Bernard Shar,
pp. 649-653, 1988..
|
Primary Examiner: Bocure; Tesfaldet
Attorney, Agent or Firm: Tripoli; Joseph S. Herrmann; Eric
P. Kurdyla; Ronald H.
Claims
We claim:
1. A signal transmission method in which an analog signal is
converted into a digital signal, transmitted in digital form and
reconverted into an analog signal and whereby said digital signal
is partitioned by means of overlapping time windows in temporally
successive blocks which are each converted into a signal sequence
representing a short-time spectrum, said method comprising the
steps of
a) windowing said digital signal and forming temporal blocks of
block length TB with overlapping regions of relative size N-1/N
where N=[2 to the power of n] 2.sup.n for whole numbers of n,
whereby overlapping blocks are selected each having a fixed number
of samples;
b) transforming said samples of each block by subjecting individual
ones of said blocks offset by TB/2*N in the time domain to a sine
or cosine transformation respectively to produce transform output
values;
c) sampling said transform output values at different positions,
causing aliasing, said sampling comprising sampling said transform
output values from N consecutive values according to a sampling
scheme: C1: 0, N, 2N, 3N . . . , or a subsampling scheme C2: N/2,
3N/2 [/ whereby four combinations with respect to transformation
and sub-scanning forms result:] resulting in four combinations
of
transformation and sampling forms K1-K4 as follows
K1: cosine transformation+selection scheme C1
K2: cosine transformation+selection scheme C2
K3: sine transformation+selection scheme C1
K4: sine transformation+selection scheme C2;
d) arranging sampled transform output values so that said aliasing
arises at predetermined positions, by applying one of said
combinations K1 . . . K4 in any arbitrary permutation on each of
overlapping blocks, whereby four groups of values with entries for
overlapping regions of blocks results, said groups of values being
differentiated by their preceding signs;
e) said arranging including selecting a combination from K1 . . .
K4 so that after inverse transformation at a receiver and summation
of the components in the signal segments of the blocks involved in
the overlap, all signals not originating from the same segment of
the original signal are compensated whereby said aliasing is
cancelled in a receiver;
f) coding, transmission and decoding said sampled/sub-sampled
transform output values of individual blocks after said
arranging;
g) subjecting decoded individual blocks to inverse sine or cosine
transformation, producing inverse transform values;
h) arranging said inverse transform values so that non-aliased
components corresponding to original input blocks are located in
respective original positions, said arranging of said inverse
transform values including segmentation of continuous-time inverse
transform signal values into successive signal segments Ni for i=1,
2, 3 . . . , which, depending on the combination K1 . . . K4 used,
contain components Ni . . . and temporally reflected alias
components Si . . . ; and
i) summing said signal segment components Ni . . . and said
temporally reflected alias components Si . . . in the signal
segments Ni of overlapping blocks.
2. A method according to claim 1, wherein:
a. said blocks are evaluated using analysis windows prior to
transformation and synthesis windows after transformation, and said
windows form segments of length TB/N equal to said signal
segments;
b. said evaluation is performed by multiplying said signal
components Ni . . . or, respectively, said temporally reflected
components Si . . . corresponding to said signal components by
components of analysis window ani . . . or, respectively,
temporally reflected components asi . . . corresponding to these
components and components of synthesis window sni . . . ; and
c. said analysis and synthesis windows fulfill the following
conditions in block overlap regions:
I. the sum of temporal regular wanted signal components of an
analysis window and synthesis window superimposed in signal
segments of a block is equal to one;
II. the sum of temporal regular aliasing components of an analysis
window and synthesis window superimposed in signal segments of a
block is equal to zero,
3. A method according to claim 2, wherein with said windows
symmetric about a block center and with double overlapping, a
synthesis window function is determined from a pre-determined
analysis window function according to the following equation:
##EQU7## for [0 less or x less or 0.5] 0.ltoreq.x.ltoreq.0.5 where
s(x) is a synthesis window function,
a(x) is an analysis window function,
x represents a standardized time with a value of 0 at the start of
a block and a value of 1 at the end of said block.
4. A method according to claim 2, wherein with said windows
symmetric about a block center and with quadruple overlapping, an
analysis window function is first determined which fulfills the
following equations:
for 0.ltoreq.x.ltoreq.0.25
where a(x) is an analysis window function, and a synthesis window
function is determined from a previously determined analysis window
function according to the following equation: ##EQU8## where sni
are components of a synthesis window function, ani are components
of an analysis window function, x represents a standardized time
with a value of 0 at the start of a block and a value of 1 at the
end of said block.
5. A method according to claim 2, wherein with said windows
symmetric about a block center and with eightfold overlapping, an
analysis window function is first determined which fulfills the
following equations:
Description
BACKGROUND OF THE INVENTION
This invention is directed to a method of transmitting a signal
using digital compression techniques. In the transmission of an
audio signal, for example, radio broadcast transmission, cable
transmission, satellite transmission and with recording devices the
analog signal is converted into a digital signal with a certain
resolution, transmitted in digital form and reconverted into an
analog signal upon reception. A greater signal-to-noise ratio is
achieved, in particular upon reproduction, by using digital
transmission.
The band width required for the transmission of such a signal is
essentially determined by the number of [scanning values] samples
per time unit which are to be transmitted. The resolution is also a
function of the number of [scanning values] samples
transmitted.
In practice it is preferable to keep the transmission band width as
narrow as possible in order to be able to transmit as many audio
signals as possible simultaneously via a wide band channel. It
would appear that the necessary band width can be reduced by
decreasing the number of [scanning values] samples or the number of
bits per [scanning value] sample. However, in general this measure
results in a deterioration in the quality of the reproduction.
A method described in DE-OS 35 06 912, improves the quality of the
reproduction by separating the digital audio signal into successive
temporal segments and transforming the audio into a short-time
spectrum which represents the spectral components of the signal for
the respective time segments. Generally, in the short-time
spectrum, for reasons of psychoacoustic laws, components which are
not perceived by the listener, i.e., are irrelevant from a
communications technology viewpoint, can be discovered more readily
than in the time domain. Upon transmission these components are
given less weight or are left out entirely. In doing this a
considerable part of the otherwise necessary data can be left out
so that the average bit rate can be considerably reduced.
To form the time segments, the signal is first evaluated in the
temporal region (time domain) using an analysis window and after
transformation, coding, transmission, decoding and inverse
transformation, is finally evaluated using a synthesis window. The
design of the analysis window influences the frequency resolution.
The advantage of a high frequency resolution is that with narrow
band signal components only a small amount of data is required for
their coding, thereby achieving a very effective bit allocation,
and the average data quantity which is needed for transmission is
considerably reduced. Therefore, for windows with "hard" edges,
such as exhibited by a rectangle, the frequency resolution is poor.
This is because the spectral components caused by the extreme rise
and fall of the signal at the start and end of the window are added
to the spectrum of the original signal in the evaluated segment.
However, the temporal segments can be joined to each other without
overlaps.
With the method described in DE-OS 35 06 912, a window function
with "softer" edges was already selected. Here, the start and the
end of the analysis window follow a cosine [square] function and
the corresponding regions of the synthesis window a sine [square]
function. The central area of both windows has a constant value.
The use of such a window function design results in an improved
frequency resolution. However, in the region of the "soft" edges
overlapping of the successive temporal segments is necessary, and
this leads to an increase in the average bit rate due to the
doubled transmission of the signals contained in this region.
A further improvement in the frequency resolution could be achieved
by using an even lower edge gradient for the window function of the
analysis window as well as by expanding the edge region within the
window. However, with these measures increased overlapping with
neighboring temporal segments is required.
If the edge region is expanded so far that the window functions no
longer have a constant value in any region, then adjacent temporal
segments must overlap each other by 50 per cent. This means that
the number of [scanning values] samples and, accordingly the
quantity of data, is doubled.
From the publication of J. P. Pfineen and A. B. Bradley
"Analysis/Synthesis Filter Bank Design Based on Time Domain
Aliasing Cancellation", IEEE Transactions, ASSP-34, No. 5, October
1986, pp. 1153 through 1161, and that of J. P. Princen, A. W.
Johnson and A. B. Bradley "Suband/Transform Coding Using Filter
Bank Design Based on Time Domain Aliasing Cancellation", IEEE Int.
Conference on Acoustics, Speech and Signal Processing 1987, pp.
2161 through 2164, it is known with a 50 per cent overlap of
successive temporal segments to reduce the quantity of data to the
original value again, in that only every second [scanning value]
sample is encoded. In the spatial domain every sample is encoded
(if data reduction is not considered). Sub-sampling is performed in
the spectral domain. The sub-sampling process is explained at page
1154 and 1155 of the Princen and Bradley reference noted above.
This proposal is based on equal window functions for the analysis
and synthesis windows. In the case of equal window functions, the
aliasing components which appear upon [sub-scanning
(]sub-sampling[)] can be compensated for by the synthesis window
after the evaluation.
It was discovered that the frequency resolution can be raised by
selecting larger overlapping regions if, at the same time, the
signal is assessed with suitable analysis and synthesis windows. In
order to reduce the climbing data rate, caused by the higher number
of [scanning values] samples, to the original value, the
sub-[scanning] would have to be performed using an even higher
factor, whereby however, further aliasing components ensue.
SUMMARY OF THE INVENTION
It is the object of the invention to specify measures for a method
for the transmission of a signal, whereby said measures are
generally applicable and also enable, with multiple overlapping
blocks, a reduction in the number of [scanning values] samples and,
therewith, in the data rate with simultaneous compensation of the
aliasing components caused by sampling in the frequency domain.
Compensation of such aliasing is achieved by arranging aliasing
Components SO as to cancel during inverse processing at a
receiver.
The method makes it possible to specify the general conditions for
the transformations of overlaps which correspond to a power of two,
i.e., for a double, quadruple, eightfold overlap, etc., and to
utilize these with a practical arrangement. Further developments of
the method provide for also determining the general conditions for
various analysis and synthesis windows and using these in practical
application.
Through applying the procedure steps according to the invention it
is possible to take advantage of the analysis characteristics of
softer analysis window functions improving with increasing
overlapping. Through corresponding sub-[scanning] sampling in the
[frequency range (frequency domain)] frequency domain, the effort
required for multiple transmission of partial window regions is
reduced to the original data rate of the [temporal] time domain
signal.
Data reduction (based on the input data rate) can be achieved using
known methods, for example as described in DE-OS 3506912. It is
herein recognized that if overlapping windows are required for
coding, the output data rate would increase in relation to the
amount of overlapping. In accordance with the principles of the
present invention there is disclosed herein a system for
significantly reducing or substantially avoiding such a data rate
increase, particularly in the case of a significant amount of
overlapping, thereby maintaining high signal quality.
[In the drawings:]
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a flow diagram with the main procedure steps of the
invention
FIG. 2 shows a graphic representation of the segmentation of the
continuous temporal signal,
FIG. 3 is a block formation from the segmented original signal,
FIG. 4 shows an even and an odd block signal component,
FIG. 5 shows a periodized even block signal component,
FIG. 6 shows [a] sub-[scanning] in the [spectrum] frequency domain
by the factor 2 and offset to the coordinates origin of TB/2 in the
time domain with cosine transformation,
FIG. 7 shows sub-[scanning] sampling in the spectrum by the factor
2 and offset to the coordinates origin of TB/4 in the time domain
with cosine transformation,
FIG. 8 shows signal components in the case of overlapping summation
for various offsets of the block start to the coordinates
origin,
FIG. 9 shows sub-[scanning] sampling in the spectrum by the factor
2, offset to the coordinates origin of TB/4 in the time domain, and
offset by half a [scanning] sampling period in the case of scanning
in the frequency domain with cosine transformation,
FIG. 10 shows signal components after transformation,
sub-[scanning] sampling transmission and inverse transformation for
various transformations,
FIG. 11 shows signal reconstruction with 50 per cent overlap,
FIG. 12 shows segmentation of analysis and synthesis windows,
FIG. 13 shows components of the analysis and synthesis windows in
the respective block region,
FIG. 14 shows signal components after transformation,
sub-[scanning] sampling, transmission and inverse transformation in
the synthesis window region for various transformations with
quadruple block overlapping,
FIG. 15 shows aliasing compensation with rectangular window for
analysis and synthesis,
FIG. 16 shows a compensation scheme for the alternating application
of sine and cosine transformation,
FIG. 17 shows double overlap in the time domain,
FIG. 18 shows quadruple overlap in the time domain,
FIG. 19 shows eightfold overlap in the time domain,
FIG. 20 shows double overlap in the frequency domain,
FIG. 21 shows quadruple overlap in the frequency domain,.
FIG. 22 shows eightfold overlap in the frequency domain.
FIG. 23 is an amplitude vs. frequency plot of spectral lines of a
short-time frequency spectrum.
FIGS. 24A-C show waveforms associated with the processing of a
sudden acoustic event.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 1 shows the method steps according to the invention. Steps
7-12 include operations which are the inverse of operations
performed in steps 1-7. Briefly, after analog-to-digital conversion
in step 1, in steps 2 and 3 overlapping blocks each having groups
of a fixed number of 1024 values are selected and subjected to a
window analysis in step 4. After window analysis the values of each
block are processed by steps 5 and 6 before coding and transmission
in step 7. This processing includes frequency transformation which
produces transform output values. The transform output values are
sampled or subsampled, causing aliasing. The sampled transform
output values are arranged so that aliasing occurs at certain
positions which result in aliasing being cancelled as a result of
inverse processing e.g., at a receiver. The coding in step 7 may
take the form of any well known data reduction technique, with the
decoding in step 7 being the inverse of the coding technique
used.
In the flow diagram illustrated in FIG. 1, the individual procedure
steps for executing the method of the invention are shown. The
[stating variable] source signal of the method forms an analog
audio signal which is converted according to procedure step 1 into
a digital signal, in which amplitude values are present as
[scanning values ] samples in digital coded form. In procedure step
2 the continuous signal is windowed, in that a series of successive
[scanning values] samples, in the ease presented here, 1024
[scanning values] samples, are selected. For example, a 1024 bit
serial-to-parallel register can be used for receiving the
continuous input sample data stream and outputting groups of 1024
samples.
In procedure step 3 blocks with temporal overlaps of 50 per cent
are formed from the selected [scanning values] samples. This means
that in adjacent blocks sometimes the same [scanning values]
samples are present, albeit in different places. Thus, the
[scanning values] samples present in the first half of a current
block correspond to the [scanning values] samples present in the
second half of the preceding block. The samples satisfy the Shannon
theory. The overlapping is caused by taking the same sample twice,
in the neighboring and overlapping blocks.
In procedure step 4 the signal segments contained in the blocks are
evaluated using analysis windows. In doing this a soft signal rise
and fall are created at the block boundaries which raises the
analysis sharpness for the following transformation. Each analysis
window is evaluated without regard to overlapping. In the
evaluation, 1024 samples (which are known to be used in other
windows) are selected and processed. This procedure is also used
for the subsequent steps of transformation (5), coding,
transmission and decoding (7) and inverse transformation (8).
Procedure step 5 forms the transformation of the existing
discrete-time signal into a discrete-frequency signal. Instead of
amplitude values, spectral values appear from now on which each
encompass a real and an imaginary component. The outputs of a sine
or cosine transform are real values. If an FFT (Fast Fourier
Transform) is used for calculating the output values, imaginary
components also result.
Next, the conversion of the spectral values into a presentation
with [pseudoquantities] pseudo amplitude values and pseudophases
takes place in procedure step 6. The spectral values are then
prepared and suited for a transmission method such as is described
in DE-OS 35 06 912. Sub-[scanning] sampling is also performed at
the same time in connection with the conversion of the spectral
values. The result is that the number of values to be transmitted
again coincides with the number of original [scanning values]
samples. The doubling of the data caused by the 50 per cent
overlapping of the blocks is, therefore, cancelled here.
In the procedure step designated 7, several individual steps are
combined encompasses the coding, if applicable the data reduction,
transmission and decoding. These procedure steps can be carried out
according to the method in DE-OS 35 06 912.
Regarding the processing in steps 6 and 7, as discussed in DE-OS
3506912, after spectral transformation in step 5 the signal is
coded in steps 6 and 7 to produce coding according to
psychoacoustic principles. By means of such psychoacoustic coding,
spectral components which are not detected at a reproduction stage,
in particular because of masking effects, are weighted less
strongly or are omitted during the coding process. This type of
processing of the short-term spectrum may readily be accomplished,
e.g., by means of a computer. FIG. 23, which will be discussed in
detail subsequently, shows the amplitude plot of spectral lines of
a short-term frequency spectrum of a signal transform at the output
of step 5. The signal coded in this manner may be transmitted via a
narrow-band transmission channel due to a reduction in the mean
data rate. The transmission channel is followed by a receiver which
performs essentially the inverse of the transmitter functions,
including decoding. An analog signal eventually produced at the
output of D/A converter 12 is not identical to an input analog
signal in step 1, because in the coding process spectral components
have been weighted differently or suppressed. The difference
between such analog signals, however, is not noticed by a listener
at the reproduction stage.
In procedure step 8 transformation inverse to that in procedure
step 5 takes place while, however, with preceding data reduction,
the signal subjected to this is a modified signal freed from
psycho-acoustically redundant components. The result of the inverse
transformation is again discrete-time signals in the form of blocks
representing signal segments of a continuous signal. However, only
half the original [scanning values] samples are present in the
blocks.
In procedure step 9, the blocks are weighted with synthesis
windows. The synthesis window functions are so designed that they
again compensate the signal distortions which have come about as a
result of the [weighting] overlapping with the analysis windows in
procedure step 4. The synthesis window itself does not compensate
for signal distortion, e.g., alias components, but its special
location and combination with the analysis window causes the
compensation. The signal distortion (alias components) is caused by
the overlapping, not by the weighting. The synthesis window
functions used here fulfill two criteria. Firstly, they complement
themselves to one in the overlap region using the corresponding
analysis windows. Secondly, the analysis window reflected in the
center of the overlap region multiplied by the synthesis window for
the block n in the difference with the analysis window reflected in
the center of the overlap region multiplied by the synthesis window
for the block n+1 in the overlap region is identical to zero. This
latter criterion contains the compensation for the aliasing
components. Steps 2 through 9 are performed serially for each block
of 1024 samples. If the required results (see, for example, FIG.
11) from step 9 are present, the addition function of step 10 can
be made, resulting in the continuous samples as indicated by step
11 (see, for example, the bottom of FIG. 11).
In procedure step 10 the blocks overlapping by 50 per cent are
added, whereby the aliasing components in the two blocks to be
superimposed appear with reversed preceding signs so that upon
addition it compensates to zero.
In procedure step 11 the formation of continuous [scanning values]
samples through joining the blocks to each other with the windowed
signal segments is illustrated.
Finally, in the last procedure step, designated 12, conversion of
the digital, coded [scanning values] samples into an analog signal
is carried out, whereby, objectively, components are in fact
missing but which, subjectively, is experienced as identical with
the original signal.
In the further explanation the cosine or, respectively, the sine
transformation is to serve as the basis of the multiply overlapping
transformations. In addition, temporal continuous signals shall be
assumed for all procedure descriptions. The transition to
discrete-time signals can, separately from the further
considerations, be carried out according to the generally known
procedure.
The cosine transformation is defined as an integral transformation
from the following pair of equations: ##EQU1##
Accordingly, the following applies for the sine transformation:
##EQU2##
The constants Ac, Be, As and Bs serve for normalizing purposes and
are not significant for the further considerations. Corresponding
to the equations (1) through (4), the temporal function f(t) for
the cosine or, respectively, the sine transformation shall only be
different from zero for the case of t larger than 0. For a
transformation with finite block length this can always be achieved
through suitable selection of the coordinates origin.
The cosine and sine transformation can be traced back to the
Fourier transformation, in that, for the cosine transformation, the
even signal component is fed to a Fourier transformation and,
respectively, the odd signal component for the sine transformation.
Using this transfer, all theorems known for the Fourier
transformation can also be utilized for the sine and cosine
transformations.
The continuous [temporal] time domain signal is divided into
segments corresponding to the block regions which, after
transformation, sub-[scanning,] sampling transmission and inverse
transformation, are fed to the overlapping summation. If the block
length is designated TB, then the segments with 50 per cent overlap
have the length TB/2, as shown in FIG. 2. The segments in temporal
[sequence] order are designated with Ni.
If blocks with 50 per cent overlap are removed from the continuous
signal so described by means of a simple rectangular window, then
there result, for example, the blocks obvious from FIG. 3 for a
cycle consisting of transformation, sub-[scanning] sampling,
transmission and inverse transformation.
If the coordinates origin is so chosen that it coincides with the
start of the transformation block, then the even or, respectively,
odd signal component of such a transformation block multiplied by
the factor 2 is, in this scheme, as shown in FIG. 4.
Here, the reflected signal components corresponding to the signal
components Ni are designated Si. The negative sign with an odd
signal component indicates that the reflected signal components
appear negative in comparison to the corresponding original
components.
The scanning of the Fourier transformed variable of the even or odd
signal component leads in the time domain to a periodizing of the
corresponding signal components. If in the time domain no aliasing
disturbance is to ensue, then the periodized signal components are
not permitted to overlap. This means that in the spectrum, a
[scanning] sampling period of Fo=1/(2TB) must be used in the
borderline case. This periodizing, with the aid of the scheme, for
example, for the cosine transformation, leads to the situation
shown in FIG. 5.
One degree of freedom, which until now was relatively arbitrarily
established, is the position of the start of the block in the used
coordinate system of the transformation. Up to now, the start of
the block coincided with the zero point of the coordinate system. A
shift in the start of the block towards positive times t in the
coordinate system and the consequences of a sub-[scanning] sampling
by the factor 2 in the spectrum, i.e., a [scanning] sampling period
of Fo=1/(2TB), is illustrated in FIGS. 6 and 7 using the example of
the cosine transformation. Shown in FIG. 6 are the various signal
components in the time domain after transformation, [subscanning]
subsampling, transmission and inverse transformation with an offset
of the transformation block from the coordinates origin of TB/2.
The signal components with an offset of TB/4 are shown in FIG.
7.
From these two examples it can be seen what influence this
important degree of freedom has on the components located in the
region which is blanked out from the periodically repeated signal
components using the synthesis window in the receiver. This time
region has the duration TB in both representations and has the
position characterized in the two pictures. The region of the
synthesis window contains, firstly, the original signal segments N1
and N2 and, secondly, the aliasing components S1 and S2. FIGS. 6
and 7 show that the offset of the start of the block from the
coordinates origin determines, on the one hand, at which point in
the block region the signal components resulting from reflection
appear but, on the other hand, has no influence on the signal
components with a noninverted temporal position.
As the method of aliasing compensation demands that the aliasing
components are compensated through summation of the block overlap
regions of the affected blocks, with double overlapping only those
signal components may be located in one half of a block which
originate from the same block half in the original signal. This
requirement is not fulfilled by a temporal offset and size of TB/2
because here reflected signal components from the second half of
the block occur in the first half and vice versa. In this case,
with a block overlap, n components, originating from the overlap
region n-1 as well as n+1, appear in the overlap region. As these
components only appear once in the respective overlap region, they
cannot compensate themselves. FIG. 8 shows, for successive blocks,
which signal components are basically involved in the summation in
the overlap region for offsets TB/2 and TB/4.
As only a temporal offset of TB/4 contains the basically correct
components, in order to, on the one hand, create the wanted signal
after a summation in the overlap region and, on the other hand, to
compensate the aliasing components, this offset of the start of the
block from the coordinates origin is used for the cosine or,
respectively, the sine transformation.
A further degree of freedom is represented by the [scanning]
sampling scheme in the frequency domain. Here, it is possible to
either let the [scanning] sampling start at the frequency f=0 or,
however, to introduce a [scanning] sampling offset corresponding to
half the [scanning] sampling period during scanning in the
frequency domain. Other offset dimensions lead to a doubling of the
data rate through an asymmetric [scanning] sampling of the
symmetrical image function for the cosine or, respectively, sine
transformation in the Fourier spectral space. The offset by half
the [scanning] sampling period with the [scanning] sampling in the
spectrum effects an alternating change in preceding sign with the
periodizing of the even or, respectively, the odd block component
after transformation, sub-[scanning] sampling, transmission and
inverse transformation in the time domain. FIG. 9 illustrates this
with the scheme used for the cosine transformation.
It can be seen from FIGS. 7 and 9 which signal components for the
cosine transformation after transformation, sub-[scanning]
sampling, transmission and inverse transformation are located in
the region which is blanked out with the synthesis window. If it is
considered that, with the sine transformation, only the reflected
components have a negative sign with regard to those with the
cosine transformation, then, for this also, the signal components
in the region of the synthesis window can be specified. In FIG. 10
the signal components located in the region of the synthesis window
after transformation, sub-[scanning] sampling transmission and
inverse transformation are specified for the four possible
transformation variations: cosine transformation with and without
[scanning] sampling offset in the spectrum as well as sine
transformation with and without [scanning] sampling offset in the
spectrum. In the case of a two-fold overlapping (N=2) of the
windows, every Nth (2nd) sample value is omitted, producing
two-fold subsampling in the transform output. In single overlapping
(N=1), every value is sampled.
The expression "reflected" as used in the preceding description
means "mirrored". The mirrored effect arises automatically if
values are samples. e.g., repeat spectra. No special use is made of
the mirrored components. The overlapping i.e., the twofold
evaluation of the input samples, together with a two fold
subsampling in the frequency domain, leads to the same number of
output samples.
In FIG. 11 the mechanism for the aliasing compensation of several
successive blocks is shown using an offset of TB/4. From the
possible transformation variations, alternating cosine and sine
transformation without [scanning] sampling offset in the frequency
domain is to be applied here with temporally successive blocks.
Thus, one of the aliasing components receives a positive sign and
the other component receives a negative sign.
In the above-mentioned example, rectangular windows were used as
analysis and synthesis window functions. However, these windows
show an extremely poor behavior with respect to selectivity in the
spectral domain. Better results are achieved if window functions
with "soft" edges are used for analysis and synthesis.
When using window functions which deviate from the rectangular
window function, two conditions must be observed.
1. the wanted signal must be correctly reconstructed by the
overlapping;
2. the aliasing disturbance must further be compensated.
In order to be able to set up the equations necessary for
maintaining these two conditions the technique to be used must
correspond and supplement the [tehnicque] technique described
above.
When the analysis window and the synthesis window are segmented in
the same way as the signal, then a situation according to that of
FIG. 12 results. Corresponding to the signal components, the
components of the analysis or, respectively, the synthesis window,
present in a temporally regular arrangement, are now designated
with an1 and sn1 respectively. Components of the analysis window,
temporally inverted owing to the reflection, are designated asi. If
the window segments, which were involved in the reconstruction of
the respective signal components, are now inserted into FIG. 11,
then a situation according to that of FIG. 13 results. The
equations, which must be met by the analysis and synthesis
functions so that, after the summation in the overlap region, the
signal is itself reconstructed on the one hand and the aliasing
disturbances are compensated on the other, can be read off from
this representation with the aid of FIG. 11.
Two equations for the regions of the block overlaps result from
FIG. 13:
If with all temporally successive transformations identical window
functions are used and if the analysis window functions are
designated a(x), where x is a standardized time which has the value
0 at the start of the block and the value 1 at the end of the
block, as well as if the synthesis function is designated with
s(x), then using the equations (5) and (6) for the overlap regions
0 less or x less or 0.5 we get:
These two equations must be fulfilled by the window functions. If
the special case is chosen in which the window functions are
symmetrical about the center of the block and it is assumed that
the analysis window function is predetermined, then a construction
rule for the synthesis window function results from the equations
(7) and (8): ##EQU3##
Following this, the method explained through the example of the
double overlap will be systematically extended to larger block
overlaps, namely the quadruple and eightfold overlap.
The degrees of freedom, shifting of the block zero point in the
temporal coordinate system and offset with the [scanning] sampling
in the spectral region are determined according to the above
considerations. This leads to a shifting of the block zero point
with respect to the coordinates origin by one eighth of the block
length TB. The offset zero and the shifting by half a [scanning]
sampling period during scanning in the spectrum are also permitted
in this case. Consequently, four transformation modifications
result from the quadruple block overlap. The signal components
located in the region of the synthesis window after transformation,
sub-[scanning] sampling, transmission and inverse transformation,
firstly using rectangular window functions for analysis and
synthesis, are shown in FIG. 14 for all valid transformations.
Similarly to the case of the double overlap, a segmentation of the
signal was carried out here with the temporal expansion of the
common overlap region of TB/4.
Under the precondition of the aliasing compensation with the
application of rectangular windows for analysis and synthesis,
there results the following temporal transformation sequence:
1. sine transformation with sub-[scanning] sampling by the factor
4, offset by TB/8 in the time domain and offset by half a
[scanning] sampling period with [scanning] sampling in the
spectrum;
2. sine transformation with sub-[scanning] sampling by the factor
4, offset by TB/8 in the time domain and no offset with [scanning]
sampling in the spectrum;
3. cosine transformation with sub-[scanning] sampling by the factor
4, offset by TB/8 in the time domain and offset by half a
[scanning] sampling period with [scanning] sampling in the
spectrum;
4. cosine transformation with sub-[scanning] sampling by the factor
4, offset by TB/8 in the time domain and no offset with [scanning]
sampling in the spectrum.
When temporal transformation sequence is employed, then, using the
scheme already used before, the situation shown in FIG. 15
results.
If we also again perform an appropriate segmentation for analysis
and synthesis windows using the designations an1, as1 and sn1 for
the individual segments in original temporal arrangement and in
temporally inverted arrangement, then we can also specify the
equations here which have to be generally fulfilled by the window
functions:
If, for reasons of simplification, it is again assumed, that the
window functions are always functions symmetric about the block
center, then a constructional rule is gained from the equations
(12) through (15) which must be met by the analysis window. This
rule is specified in a form whereby x again corresponds to the
standardized time. It is summarized in the equations (16) and
(17):
for [0</=x</=0.25] 0.ltoreq.x.ltoreq.0.25
By specifying an analysis window which meets the rules (16) and
(17), a corresponding synthesis window can be calculated using the
system of equations (1*): ##EQU4##
If it is not assumed that an aliasing compensation is to be present
with the application of rectangular windows but, rather, that the
aliasing components only compensate when using a certain window
function which is different from a rectangular window, then we can
deviate from the temporal transformation sequence specified above
and apply any arbitrary transformation sequence. By using another
transformation sequence the equations (10) through (15) alter if
necessary and hence the constructional rules for analysis and
synthesis windows. However, as the signal components with all
transformations are the same in the region of the synthesis window
and are merely differentiated by their preceding signs, the
structure of the equations (10) through (15) with their segments of
analysis and synthesis windows remains and only the signs in these
six equations alter through a temporally different transformation
sequence. However, this means for the constructional rule in
equations (16) and (17), which must be met by the analysis window,
that here there are basically only two different rules. Firstly,
the one specified in equations (16) and (17); secondly, one with a
negative sign on one side of the equals sign in both equations. As
an example of such a case the alternating application of sine and
cosine transformation without [scanning] sampling offset in the
spectrum is to be specified. FIG. 16 illustrates the scheme with
this transformation sequence with the precondition of rectangular
windows for analysis and synthesis.
The equations for the analysis and synthesis windows then read
accordingly:
and hence the constructional rule for the analysis window:
for [0</=x</= or 0.15] 0.ltoreq.x.ltoreq.0.15.
The considerations made in conjunction with the quadruple overlap
can be systematically transferred to higher degrees of overlapping,
for example, the eightfold overlap. The offset between the start of
the block and the zero point of the coordinate system now has the
size TB/16. Furthermore, again only the four transformation
variations can be used like with the quadruple block overlap. It is
also valid that the temporal transformation sequence only has an
influence on the preceding signs of the signal components, not,
however, on their temporal position in the region of the synthesis
window after transformation, sub-[scanning] sampling, transmission
and inverse transformation.
Fourteen (14) equations which must be fulfilled by analysis and
synthesis windows result from similar considerations for the
following transformation sequence:
1. sine transformation with sub-[scanning] sampling by the factor
4, offset by TB/8 in the time domain and offset by half a
[scanning] sampling period with [scanning] sampling of the
spectrum;
2. sine transformation with sub-[scanning] sampling by the factor
4, offset by TB/8 in the time domain and no offset with [scanning]
sampling of the spectrum;
3. cosine transformation with sub-[scanning] sampling by the factor
4, offset by TB/8 in the time domain and offset by half a
[scanning] sampling period with [scanning] sampling of the
spectrum;
4. cosine transformation with sub-[scanning] sampling by the factor
4, offset by TB/8 in the time domain and no offset with [scanning]
sampling of the spectrum;
Three equations, to be understood as conditions to be fulfilled by
the analysis window, can be extracted from this. The conditions are
as follows with the precondition of axis-symmetrical analysis and
synthesis window functions:
If a window function a(x) is found which fulfills the above three
conditions, then the synthesis window can be calculated via the
system of equations (30): ##EQU6##
The solutions for the calculation of analysis and synthesis windows
of the various block overlaps, given in the preceding sections,
exhibit a systematic construction. This can be clearly recognized
in the matrix equations (18) and, the conditions which the analysis
window function must fulfill bring, with increasing overlapping,
greater restrictions for a sensible window design.
For the uniform comparison of the various block overlaps, a Kaiser
window was selected as the basis. The Kaiser window was modified so
that it satisfies the respective conditions for the overlapping
transformation. This always happened through an expansion
corresponding to the window conditions upon pre-determination of
the Kaiser window function in a partial region of the window. In
the case of the double overlap, the degrees of freedom for the
analysis window are so large still that a complete Kaiser window
can be selected here (FIG. 17). In the case of the quadruple
overlap, the Kaiser window must be modified owing to the restricted
degrees of freedom as described by equations (16) and (17). With
the window construction in FIG. 18, a Kaiser window was
pre-determined between the standardized time values x=1/8 and x=7/8
and the remaining window parts jointed on via the equations (16)
and (17). As with increasing overlapping the restrictions for the
analysis window become larger and larger, the Kaiser window can, in
the case of the eightfold overlap (FIG. 19), only be pre-determined
between x=1/4 and x=3/4. The remaining window parts must then be
calculated by means of equations (27) through (29).
FIGS. 17 through 22 show the temporal progression of the window
function and the amount of the Fourier spectrum. The windows are so
designed that the effective width of the window, i.e., the width of
the window in which almost the entire energy of the window lies, is
the same for all overlap sizes. This window width corresponds to
the window width of the double overlap. The nominal window width
doubles for every doubling of the overlap, as shown in FIGS. 17
through 19.
By choosing the Kaiser window as the analysis window function, the
corresponding synthesis windows receive a camber greater than one.
This behavior must be considered when optimizing the windows on the
basis of the respective application because, if applicable,
disturbing components, which ensue upon coding the spectrum, can be
slightly increased through this If all three time functions of the
analysis window are compared with each other, then the almost
identical progression in the region of the effective window width
can be clearly seen. From this there results, in the spectrum, an
identical width for the "main slope" of the amount progression for
the Fourier transformed variable of the analysis window function.
In FIGS. 20 through 22, the influence which the multiple overlap
has on the chosen example can be clearly recognized. Ever smaller
window edge values results from the respective doubling of the
overlap and the lengthening of the original Kaiser window connected
with this. Through this effect there results, in the spectrum, even
greater attenuation into which the spectral progression grades
after the "main slope". The window family should only be regarded
as an example for the way of operation of the multiple overlap. The
window design must be matched to the respective application case.
This means, for example, for an analysis window for the eightfold
overlap, that through appropriate design the "main slope" becomes
narrower if not such a large attenuation is required after the
"main slope".
FIG. 23 shows the amplitude plot of the spectral lines of a
short-time frequency spectrum, as obtained at the output of state 5
in FIG. 1. The whole frequency band of the short-time spectrum
f1-f15 is subdivided into a plurality of frequency groups f1-f2,
f2-f4, f4-f12, f12-f14 and f14-f15. In the individual frequency
groups, the spectral lines are examined and weighted according to
psychacoustic principles. Only the dominant amplitude values are
transmitted, irrelevant amplitude values are weighted less strongly
or suppressed. The absolute maximum 15 of the whole frequency band
is first transmitted as an absolute value with 12-16 bits. The
maxima 14, 16, 17, 18 of the remaining frequency groups are
transmitted with an accuracy of 8 bits, i.e., in their relative
position to absolute maximum 15. The remaining values 20-26 of the
frequency group f4-f12 are related to maximum value 16, i.e. their
deviation from maximum value 16 is transmitted. To this end the
amplitude range is starting from maximum 16, subdivided into three
ranges A1, A2, A3 each of 10 dB and one range A4 for the remainder.
Signal values 16, 20, 21 or 22, 23 or 24 or 25, 26, lying in each
case in an amplitude range are transmitted as an identical value.
No distinction is therefore drawn between values 16, 20, 21 and 22,
23 and 25, 26. The amplitude values 25, 26 at frequencies f10, f11
which fall below the value of 30 dB below maximum 16, are set at
zero. The phase of values 25, 26 is not transmitted. These spectral
components would, because of their close position to value 16 and
their small amplitude, in any case no longer be detectable by
virtue of the masking effect. In practice, the whole frequency band
f1-f15 is divided into 26 frequency groups, of which only 5 are
shown in FIG. 23 for the sake of simplicity. Due to dividing into
amplitude ranges A1, A2, A3, A4, a total of 2 bits is sufficient
for the transmission of amplitude values 20-26 relative to maximum
16. For each transmitted amplitude value which lies in the ranges
A1 to A3, 2 bits are transmitted for the associated phase
value.
A considerable reduction in the amount of data required for
transmission is already achieved by the coarse quantization of the
amplitude and phase values with 2 bits. An additional saving of
bits is also made during transmission by dropping components,
namely the phase values for amplitude values 25, 26 in frequency
group f4-f12. The liberated bits may be used for the transmission
of a more detailed amplitude subdivision in ranges A1-A3. To this
end, for example, each range A1-A3 is divided into two ranges of 5
dB each. Moreover, there is assigned to each frequency value 20-24
a bit which indicates whether the amplitude value, e.g. 20, 21,
lies within the first 5 dB or the second 5 dB below maximum 16. The
assignment of these bits takes place on the basis of a table 28
which is created at the transmitter and is reconstructable at a
receiver. To this end there is placed over the whole plot of the
frequency spectrum in FIG. 23 a grid 27 with gradation in stages of
6 dB. Amplitude values 20-24 are therefore assigned to this grid.
Table 28 assigns to each amplitude value 20-24 a particular
position in relation to maximum 16. Table 28 begins with the lowest
frequency value and shows by means of the line the respective
position in relation to the maximum of the corresponding frequency
range.
If further free bits are available, a subdivision of the 5 dB
ranges into 2.5 dB ranges will be carried out. The subdivision
process may be continued indefinitely. The saving of bits and the
use of these bits for refinement of resolution is termed adaptive
quantization.
FIG. 24A shows the pre-processing of a sudden acoustic event
waveform 29 which occurs within a time window t1-t7 at a point in
time t9. Such an acoustic event may be e.g. the striking of a
musical instrument such as a triangle. The pre-processing takes
place prior to step 5 frequency transformation. Acoustic event 29
is also preceded by a preshoot between t8 and t9, which is
inaudible due to a preliminary masking. During conversion into the
frequency spectrum in stage 5 in FIG. 1 there arises in each case
in the frequency domain a signal which indicates the spectral
distribution in window t1-t7. Since in the case of said signal the
assignment of spectral lines to individual points in time within a
time window no longer takes place, event 29 averaged over the whole
time window t1-t9 would therefore seem to be blurred. An audible
distortion may occur as a result.
In order to prevent this possible defect, a time window t1-t7 or
block is subdivided into 32 sub-blocks as shown in FIG. 24B. The
amplitudes of the individual sub-blocks are determined. As soon as
an amplitude increase of more than 20 dB occurs between two
sub-blocks, produced in FIG. 24 by event 29, an additional measure
will be triggered as shown in FIG. 24C. This measure consists in
the fact that prior to the amplitude increase the signal is by
means of a companding process, increased at the transmitter and
correspondingly reduced again at the receiver. The above-mentioned
defects caused by the blurring of the short-time event over the
whole time window will thereby be reduced.
* * * * *